The Perron integral and existence and uniqueness theorems for a first order nonlinear differential equation
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- by Manoug N. Manougian
- Proc. Amer. Math. Soc. 25 (1970), 34-38
- DOI: https://doi.org/10.1090/S0002-9939-1970-0255881-2
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Abstract:
The Perron integral is used to establish an existence and uniqueness theorem concerning the initial value problem $y’(t) = f(t,y((t))$, and $y({t_0}) = \alpha$, for $t$ on the interval $I = \{ t|0 \leqq t \leqq 1\}$. The existence and uniqueness of the solution is obtained by use of a generalized Lipschitz condition, and a Picard sequence which is equiabsolutely continuous on $I$. Also, we prove a theorem on the uniqueness of solution by a generalization of Gronwall’s inequality.References
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Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 34-38
- MSC: Primary 34.04
- DOI: https://doi.org/10.1090/S0002-9939-1970-0255881-2
- MathSciNet review: 0255881